Optical position-measuring device

ABSTRACT

In an optical position-measuring device for acquiring the rotational angle between two objects that are rotationally moveable relative to each other, a grating measuring standard rotating about an axis of rotation is arranged as a reflection grating. Position information both about an azimuthal rotary movement about the axis of rotation and about a radial displacement of the grating measuring standard is able to be obtained. At least one detection unit is used for scanning the rotating grating measuring standard in order to determine the azimuthal rotational angle as well as a radial displacement of the grating measuring standard. The neutral pivot points of the scanning of the grating measuring standard for the determination of the rotational angle and the displacement are situated in the same plane, with this plane being situated in parallel with the grating measuring standard. The neutral pivot point denotes the particular location about which the grating measuring standard or the detection unit is able to be tilted without a position offset.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims priority to Application No. 10 2019 210274.3, filed in the Federal Republic of Germany on Jul. 11, 2019, whichis expressly incorporated herein in its entirety by reference thereto.

FIELD OF THE INVENTION

The present invention relates to an optical position-measuring device,e.g., for acquiring the rotational angle between two objects that areable to rotationally move relative to each other.

BACKGROUND INFORMATION

Generally, such position-measuring devices have a grating measuringstandard, which rotates about an axis of rotation and is situated onwhat is referred to as a graduated disk. The grating measuring standardis usually arranged as a radial graduation, which, when scanned with theaid of a suitable scanning unit, makes it possible to generate positionsignals with regard to the rotary movement of the graduated disk. Thegenerated position signals characterize the azimuthal rotational anglebetween the two objects that are rotationally movable relative to eachother. Among other things, the scanning unit required for this purposeincludes at least one appropriately arranged optoelectronic detectorsystem. The two objects whose position or angular relative orientationwith respect to each other is to be determined are connected to therotating graduated disk on the one hand and to the stationary part ofthe position-measuring device on the other hand. In a typicalapplication, for example, the rotary movement of a rotating drive shaftin relation to the stationary drive housing is determined with the aidof such a position-measuring device. The position signals or rotationalangles acquired in this manner are able to be utilized in a conventionalmanner for the drive control.

Problems may arise, for example, if the rotating graduated disk and thestationary components of the position-measuring device are not alreadyassembled relative to one another at the factory but, for instance, theassembly of the separately delivered graduated disk and the scanningunit(s) is carried out by the customer. In such a case, it may notalways be ensured that the graduated disk and thus the scanned gratingmeasuring standard are mounted in a precisely centered manner relativeto the actual axis of rotation. However, this is an importantprecondition for the evaluation of the generated position signals. Inpractice, position signals that include what are referred to aseccentricity errors are therefore often produced. These eccentricityerrors, which lie in the range of the eccentricity, are attributable tothe fact that the actual axis of rotation does not coincide with theaxis of the rotating graduated disk or grating measuring standard. Theerrors caused by an eccentric mounting of the graduated disk in anassembly at the customer site are considerable and significantly affectthe maximum measuring accuracy of the corresponding position-measuringdevices.

The corresponding correlations will be described in more detail withreference to FIGS. 1A to 1D, each of which illustrates a graduated diskTS, rotating about axis of rotation MD, in different rotationalpositions A to D, with axis M_(TS) of the grating measuring standard orgraduated disk TS having an eccentricity e with respect to axis ofrotation MD. In addition, each of FIGS. 1A to 1D illustrates theeccentricity-related rotational angle error Δφ_(ecc)(Θ) in thecorresponding rotational position A to D of graduated disk TS. Thegrating measuring standard on graduated disk TS, is arranged as a radialgraduation and is situated in the form of a ring-shaped graduation trackin the middle of scanning radius R about axis M_(TS) of the gratingmeasuring standard or graduated disk TS.

In such a case, the tangential displacement Δt (Θ) of graduated disk TSat the scanning location of the grating measuring standard results asfollows:

Δt(θ)=e·sin(θ+Δθ₁)  (Eq.1)

in which Δt (Θ) represents the tangential displacement of the graduateddisk, θ represents the rotational angle of the graduated disk, erepresents the eccentricity, and ΔΘ₁ represents the phase position ofthe eccentricity-related rotational angle error.

The azimuthal scanning of the grating measuring standard on graduateddisk TS supplies a rotational angle value φ_(meas)(Θ), which has arotational angle error Δφ_(ecc)(Θ) caused by the present eccentricity e,according to the following relationship:

(φ_(meas)(θ)=θ+Δ_(ecc)(θ)  (Eq. 2)

in which:

$\begin{matrix}{{{\Delta\phi}_{ecc}(\theta)} = {\frac{\Delta {t(\theta)}}{R} = {\frac{e}{R} \cdot {\sin ( {\theta + {\Delta\theta}_{1}} )}}}} & ( {{Eq}.\mspace{11mu} 3} )\end{matrix}$

and in which φ_(meas)(Θ) represents the rotational angle value of theazimuthal scanning, Δφ_(ecc)(Θ) represents the eccentricity-relatedrotational angle error, θ represents the rotational angle of thegraduated disk, e represents the eccentricity, ΔΘ₁ represents the phaseposition of the eccentricity-related rotational angle error, and Rrepresents the scanning radius.

As illustrated in FIGS. 1A to 1D, and also indicated in Equation 3, theeccentricity-related rotational angle error Δφ_(ecc)(Θ) is periodic andrepeats at the periodicity of a full rotation of graduated disk TS. Inrotational positions A and C of graduated disk TS according to FIGS. 1Aand 10, the eccentricity-related rotational angle error Δφ_(ecc)(Θ) ismaximal, and in rotational positions B and D of graduated disk TSaccording to FIGS. 1B and 1D, eccentricity-related rotational angleerror Δφ_(ecc)(Θ) disappears.

There are a number of conventional approaches that are intended toaddress eccentricity errors in rotatory position-measuring devices. Forexample, German Patent Document No. 11 2005 002 253, and U.S. Pat. No.7,187,305, provide that, in addition to the ring-shaped graduationtrack, which is used to acquire the rotational movement and has a radialgraduation and an associated detection unit or scanning point, a furtherring-shaped graduation track is positioned in parallel, which includesgraduation or grating lines placed in a concentric and ring-shapedmanner. Via an additional detection unit, which is allocated to theadditional graduation track and situated in the same azimuth position asthe first detection unit, a possibly existing deflection of thegraduated disk in the radial direction is able to be acquired inquantitative terms and utilized for correcting the position signals orrotational angles of actual interest and which describe the rotation ofthe graduated disk about the axis of rotation.

In the following text, the principle for correcting eccentricity errorson which German Patent Document No. 11 2005 002 253, and U.S. Pat. No.7,187,305, is based is described with reference to FIGS. 2A to 2D. FIG.2A to 2D illustrate graduated disk TS including two graduation tracksS1, S2 and associated detection units D1, D2 in different rotationalpositions A to D, with axis M_(TS) of the grating measuring standard orgraduated disk TS having an eccentricity e relative to axis of rotationMD. FIGS. 2A to 2D also illustrate the eccentricity-related deflectionsΔr_(ecc)(Θ) of graduated disk TS in the radial direction (upperillustration) and eccentricity-related rotational angle errorsΔφ_(ecc)(Θ) (lower illustration) for the respective rotational positionA to D.

In the case of an eccentric movement of graduated disk TS, its radialdeflection Δr_(ecc)(Θ) is linked with tangential displacement Δt(Θ) bythe following relationship:

$\begin{matrix}{{\Delta {r_{ecc}(\theta)}} = {\Delta {t( {\theta + \frac{\pi}{2}} )}}} & ( {{Eq}.\mspace{11mu} 4} )\end{matrix}$

in which Δ_(ecc)(Θ) represents the radial deflection of the graduateddisk, Δt(Θ) represents the tangential displacement of the graduateddisk, and θ represents the rotational angle of the graduated disk.

Thus, the following relationship applies to eccentricity-relatedrotational angle error Δφ_(ecc)(Θ):

$\begin{matrix}{{{\Delta\phi}_{ecc}(\theta)} = {{\frac{1}{R} \cdot \Delta}\; {r_{ecc}( {\theta - \frac{\pi}{2}} )}}} & ( {{Eq}.\mspace{11mu} 5} )\end{matrix}$

in which Δφ_(ecc)(Θ) represents the eccentricity-related rotationalangle error, Δr_(ecc)(Θ) represents the radial deflection of thegraduated disk, R represents the scanning radius, and θ represents therotational angle of the graduated disk.

As illustrated in FIGS. 2A to 2D, the measured value of the radialgraduated disk deflection Δr_(ecc)(Θ), obtained by scanning thegraduation lines in graduation track S2 arranged in ring-shaped form, isphase-shifted by precisely 90° relative to eccentricity-relatedrotational angle error Δφ_(ecc)(Θ). This correlation may be utilized fora correction in that the measured value of radial graduated diskdeflection Δr_(ecc)(Θ) is recorded for a full rotation of graduated diskTS during a calibration operation after the installation of graduateddisk TS, is further processed and scaled in the process by the factor1/R and stored as a rotational-angle-dependent correction value _(corr)(Θ), e.g., in a table, according to the following relationship:

$\begin{matrix}{{\phi_{corr}(\theta)} = {{\frac{1}{R} \cdot \Delta}\; {r_{ecc}(\theta)}}} & ( {{Eq}.\mspace{11mu} 6} )\end{matrix}$

in which φ_(corr)(Θ) represents the rotational-angle-dependentcorrection value, Δr_(ecc)(Θ) represents the radial deflection of thegraduated disk, R represents the scanning radius, and θ represents therotational angle of the graduated disk.

During the measuring operation, the actually output and correctedangular position φ_(out) is corrected with the aid of a correction valueφ_(oorr)(Θ), offset by 90°, from the table.

By proceeding in this manner, no external reference system is requiredfor the calibration of the azimuthal rotational angle value. Instead,the position-measuring device ascertains all required correctioninformation on its own.

For optical position-measuring devices that operate using transmittedlight, it is thereby possible to correct the measuring errors caused bya possible eccentricity of the graduated disk or the grating measuringstandard. However, in particular in the case of rotatory opticalposition-measuring devices using incident light scanning, still furthererrors result that may have a considerable adverse effect on themeasuring accuracy. Such errors are caused by a possible tumbling motionof the graduated disk if it is not ideally positioned or supported.German Patent Document No. 11 2005 002 253, and U.S. Pat. No. 7,187,305,do not provide any solutions for correcting errors of the foregoingtype.

SUMMARY

Example embodiments of the present invention provide an opticalposition-measuring device, or optical position encoder, for acquiringrelative rotational movements by which not only eccentricity-relatederrors during the rotational angle determination are able to becompensated for but also errors that are caused by tumbling of thescanned grating measuring standard or graduated disk.

According to an example embodiment of the present invention, an opticalposition-measuring device, for acquiring the rotational angle betweentwo objects that are able to rotate relative to each other, includes agrating measuring standard, which rotates about an axis of rotation andis arranged as a reflection grating and from whose scanning positioninformation both about an azimuthal rotary movement about the axis ofrotation and about a radial displacement of the grating measuringstandard is able to be generated. In addition, at least one detectionunit for scanning the rotating grating measuring standard is provided inorder to determine the azimuthal rotational angle as well as a radialdisplacement of the grating measuring standard. In this context, theneutral pivot points of the scanning of the grating measuring standardfor determining the rotational angle and the displacement are situatedin the same plane, with this plane being situated in parallel with thegrating measuring standard, and the neutral pivot point denoting theparticular location about which the grating measuring standard or thedetection unit is able to be tilted without a position offset.

It is possible that the grating measuring standard includes a radialgraduation as well as an annular graduation situated next to it.

A first detection unit is able to be used for scanning the radialgraduation and a second detection unit is able to be used for scanningthe annular graduation.

It is furthermore possible that the grating measuring standard includesstripe elements, which are disposed in an annular and periodic manner ata first measuring standard periodicity, with the stripe elements havinga radial orientation in the longitudinal extension direction, and forthe absolute position encoding, the stripe elements have a periodicstructure with a second measuring standard periodicity along theirlongitudinal extension direction.

The detection unit may have a single light source as well as a singledetector system.

The detector system may be arranged as a two-dimensional detector systemwith a plurality of detector elements and a plurality of detectorcolumns having multiple detector elements in each case, with thedetector columns being periodically disposed at a first detectionperiodicity along the ring-shaped placement direction, and the detectorelements in the detector columns being periodically arranged at a seconddetection periodicity.

The optical scanning of the grating measuring standard may be providedas central projection scanning using the image scale β=2, and mayinclude a divergent light source as well as a detector system, which hasa periodic arrangement along at least one direction.

In addition, the optical position-measuring device may include a signalprocessing unit, which is configured and arranged such that: therotational-angle-dependent measured values, obtained during acalibration operation across at least one full rotation of the gratingmeasuring standard, are further processed into a radial displacement ofthe grating measuring standard and are able to be stored asrotational-angle-dependent correction values in a memory of the signalprocessing unit; and the rotational-angle-dependent correction valuesstored in the memory are utilized by the signal processing unit in ameasuring operation for correcting the measured azimuthal rotationalangle with regard to existing eccentricity and tumbling errors.

The signal processing unit may be configured and arranged so that thatthe rotational-angle-dependent measured values with regard to a radialdisplacement of the grating measuring standard, obtained during acalibration operation, are utilized by the signal processing unit duringa measuring operation for the correction of a rotational angle, offsetby 90°, with regard to existing eccentricity and tumbling errors.

The signal processing unit may correct the rotational angle for existingeccentricity and tumbling errors, according to the followingrelationship:

φ_(out)=φ_(meas)−φ_(corr)((φ_(meas)−π/2)

in which φ_(out) represents the output, corrected angular position,φ_(meas)(Θ) represents the rotational angle value of the azimuthalscanning, and φ_(corr)(Θ) represents the rotational-angle-dependentcorrection value.

By the measures described herein, the rotational angle measured by theposition-measuring device is able to be corrected both for possiblyexisting eccentricity errors and simultaneously also for possibletumbling errors of the grating measuring standard or graduated disk. Thelatter constitute a considerable error source, in particular in the caseof optical position-measuring devices featuring incident-light scanning.

Using a particular grating measuring standard, the information requiredfor this purpose is able to be obtained from a single scanning point. Avery compact configuration of the corresponding position-measuringdevice may therefore be obtained.

Further features and aspects of example embodiments of the presentinvention are described in more detail below with reference to theappended Figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A to 1D illustrate an eccentrically disposed graduated disk indifferent rotational positions in each case and the respectiveassociated eccentricity-related angular deviations.

FIGS. 2A to 2D illustrate an eccentrically disposed graduated diskhaving an additional graduation track, in different rotationalpositions, according to a conventional arrangement, and also therespective associated radial graduated disk deflections and rotationalangle errors.

FIG. 3 illustrates the relationships in the case of a tumbling graduateddisk during incident-light scanning.

FIGS. 4A to 4D illustrate the influence of a tumbling graduated disk onthe measured rotational angle, similar to the illustrations provided inFIGS. 1A to 1D.

FIG. 5 illustrates the errors in the measured rotational angle caused byeccentricity and tumbling.

FIGS. 6A to 6C illustrate the neutral pivot point in a first scanningarrangement.

FIGS. 7A to 7C illustrate the neutral pivot point in a second scanningarrangement.

FIGS. 8A and 8B illustrate the procedure during a calibration andmeasuring operation of the position-measuring device.

FIG. 9A is a top view of a graduated disk of a position-measuring deviceaccording to an example embodiment of the present invention.

FIG. 9B is a cross-sectional view of the position-measuring devicehaving the graduated disk illustrated in FIG. 9A.

FIG. 10A is a top view of the graduated disk of a position-measuringdevice according to an example embodiment of the present invention.

FIG. 10B is a cross-sectional view of the position-measuring devicehaving the graduated disk illustrated in FIG. 10A.

DETAILED DESCRIPTION

According to German Patent Document No. 11 2005 002 253, and U.S. Pat.No. 7,187,305, each of which is expressly incorporated herein in itsentirety by reference thereto, mentioned above, rotatory opticalposition-measuring devices having grating measuring standards that arescanned using transmitted light substantially exhibit only eccentricityerrors as an error contribution to a position determination. In the caseof rotatory optical position-measuring devices featuring incident lightscanning, an additional error contribution is present as well, which iscaused by a possible tumbling motion of the grating measuring standardor graduated disk. Such a tumbling motion may occur when the graduateddisk in the respective measuring system is not correctly supported ormounted.

The effect of a tumbling graduated disk scanned using incident light onthe position measurement is described with reference to FIG. 3. Theupper portion of FIG. 3 provides a schematic top view of graduated diskTS, and the lower portion of FIG. 3 provides a schematic side view ofthe position-measuring device. Indicated in the form of a dashed line inthe lower portion of FIG. 3 is correctly mounted graduated disk TSwithout any tumbling motion, and the solid line indicates graduated diskTS′, which is tilted about pivot point D, i.e., a tumbling graduateddisk.

In the side view, tumbling graduated disk TS' is illustrated in FIG. 3by a normal vector N, which is tilted in this view. The light-sensitivearea of detection unit DET is situated in scanning plane AE, andscanning beam bundles AS, which are only schematically indicated andemitted by a light source in detection unit DET, are reflected bygraduated disk TS′, which is tilted in the illustrated state, and alight pattern generated via the scanning impinges upon detection unitDET with an offset. This means that detection unit DET acquires aposition that is offset, i.e., deviates, from the true position. Ifgraduated disk TS rotates, the tip of normal vector N of graduated diskTS describes a circular path about pivot point D, as illustrated in theupper portion of FIG. 3.

Analogous to the above discussion relating to FIGS. 1A to 1D, it is alsopossible to illustrate the effect of a possible tumbling motion ofgraduated disk TS on the resulting measuring error. This is illustratedin FIGS. 4A to 4D.

As illustrated in FIGS. 4A to 4 d, the tumbling-related rotational angleerror Δφtilt is maximal in rotational positions A and C of graduateddisk TS. In rotational positions B and D, on the other hand, in whichonly a radial displacement of the light pattern is present,tumbling-related rotational angle error Δφtilt vanishes.

In an incident light scan, rotational angle error Δφ_(tilt), caused bythe tumbling motion of graduated disk TS, is described by the followingrelationship:

Δφ_(tilt) =b·sin(θ30 Δθ₂)  (Eq. 7)

in which Δφ_(tilt) represents the tumbling-related rotational angleerror, b represents the amplitude of the tumbling-related rotationalangle error, θ represents the rotational angle of the graduated disk,and ΔΘ₂ represents the phase position of the tumbling-related rotationalangle error.

Overall, the total measuring error Δφ_(total) during the positiondetermination results from the sum of the eccentricity- andtumbling-related components of rotational angle error Δφ_(ecc),Δφ_(tilt) according to relationships 3 and 7, as follows:

Δφ_(total)=Δφ_(ecc)=α·sin(θ+Δθ₁)+b·sin(θ+Δθ₂)  (Eq. 8)

in which Δφ_(total) represents the total measuring error, Δφ_(ecc)represents the eccentricity-related rotational angle error, Δφ_(tilt)represents the tumbling-related rotational angle error, a (which equalse/R) represents the amplitude of the eccentricity-related rotationalangle error, b represents the amplitude of the tumbling-relatedrotational angle error, θ represents the rotational angle of thegraduated disk, ΔΘ₁ represents the phase position of theeccentricity-related rotational angle error, and ΔΘ₂ represents thephase position of the tumbling-related rotational angle error.

FIG. 5 illustrates the different components of rotational angle errorΔφ_(ecc), Δφ_(tilt) as well as the resulting total measuring errorΔφ_(total) according to relationship 8 across an entire graduated diskrotation. The phase positions and amplitudes of the eccentricity-relatedrotational angle errors Δφ_(ecc) and the tumbling-related rotationalangle errors Δφ_(tilt) have been selected so that they do not agree andthe phase position of total measuring error Δφ_(total) therefore alsodiffers from the phase positions of the different error components. Asillustrated in FIG. 5, resulting total measuring error Δφ_(total) alsohas a periodicity of 360°.

To allow for a simultaneous and reliable correction of the eccentricity-and tumbling-related rotational angle errors Δφ_(ecc), Δφ_(tilt) duringthe incident light scanning of a rotating grating measuring standard,certain measures are required with regard to the provided scans, inparticular if the correction mechanism described in German PatentDocument No. 11 2005 002 253, and U.S. Pat. No. 7,187,305, mentionedabove, is to be used. Important in this context is the position of thatwhich is referred to as the neutral pivot point of the scanning fordetermining the rotational angle and displacement. The meaning of theneutral pivot point of a scanning operation is described in more detailbelow with reference to two different optical scanning alternatives.

FIGS. 6A to 6C illustrate the case of a first optical scanning for whichthe neutral pivot point of a scanning operation is to be described, forexample.

FIG. 6A schematically illustrates the optical scanning of a reflectivegrating measuring standard on a scale T with the aid of a scanning unitAEH. Situated in scanning unit AEH is a light source LQ, the light ofwhich is collimated by a collimator lens KL and impinges upon thegrating measuring standard on scale T. The radiation reflected by scaleT reaches a sensor S in scanning unit AEH, which is disposed at ascanning distance d above scale T. The center beam of collimator lens KLand the two edge beams that are incident on scale T at points P, Q, andR are explained as an example of the scanning beam characteristic. Asillustrated, the radiation reflected by points P, Q, and R on scale Timpinge upon points P′, Q′, and R′ on sensor S.

In the event that scale T is tilted, the resulting radiationcharacteristic of the respective scanning now depends on the particularpoint or the particular axis of rotation DA about which scanning unitAEH is rotated or tilted. In the case of FIG. 6B, axis of rotation DAabout which tilting at an angle R_(y) results is located in point Q andthus on scale T. Since the angle of incidence in the selected scanningis identical with the angle of emergence, in a tilted position the beamreflected by point Q no longer impinges upon point Q′ on sensor S, as inan untitled case, but upon point Q″, offset by an amount Δx, in thedetection plane of sensor S. In a similar manner, in the tilted state,the beams reflected by points P and R on scale T impinge upon points P″and R″, respectively, in sensor S. The magnitude of the tilting-relatedoffset Δx is basically able to be precisely indicated in the form of anequation but is of no importance for the following observations. In thefinal analysis, the tilting about rotational axis DA thus causes sensorS to detect a position offset because the light pattern has traveledfurther on sensor S as a result of the tilting, although scanning unitAEH is still positionally situated at the same x-position.

In order to illustrate the importance of the respective position of axisof rotation DA about which tilting results, FIG. 6C illustrates the casewhere axis of rotation DA is situated at a distance 2 d from the surfaceof scale T. If scanning unit AEH is rotated at an angle R_(y) about theaxis of rotation DA situated there, the beams reflected at points P, Q,and R on scale T impinge upon points P′, Q′, and R′ on sensor S, as inthe non-tilted state according to FIG. 6A. In this position ofrotational axis DA, no position offset is therefore detected despite thetilting of scanning unit AEH.

Thus, it is apparent that in the scanning illustrated in FIGS. 6A to 6C,an axis of rotation DA or a point exists in the system about whichscanning unit AEH is able to be tilted without causing a change inposition in the process. The corresponding axis of rotation DA willhereinafter be termed the neutral axis of rotation and the correspondingpoint will be termed the neutral pivot point. In the described exampleillustrated in FIGS. 6A to 6C, the neutral pivot point is situated attwice the scanning distance 2 d from the surface of scale T.

In the following text, the neutral pivot point will additionally also bedescribed, for example, with reference to FIGS. 7A to 7C in connectionwith a further scanning in an optical position-measuring device. In thiscase, in contrast to the preceding example, no shadow-cast scanning isprovided, and scale T is imaged through an imaging lens AL onto sensorS. In the illustrated example of FIGS. 7A to 7C, 1:1 imaging or an imagereversal is present, so that points P, Q, and R situated on scale T areimaged onto sensor S in the reverse order R′, Q′, P′. For reasons ofbetter clarity, only the beam characteristic for central point Q isillustrated.

FIG. 7B illustrates the situation where axis of rotation DA extendsthrough point Q on scale T and scanning unit AEH is tilted by angleR_(y) about axis of rotation DA. Since an imaging system is involvedhere, point Q is once again imaged to point Q′ in sensor S, regardlessof the changed illumination direction.

A different situation is encountered if axis of rotation DA extendsthrough point Q′ situated in sensor S. In FIG. 7C, tiling at angle R_(y)about this axis of rotation DA is illustrated. Since the object to beimaged, i.e., point Q on scale T, moves away from the optical axis ofimaging lens AL during the tilting, this point Q is also imaged at anoffset in the amount of Ax to point Q″ on sensor S.

In the scanning example illustrated in FIGS. 7A to 7C, a differentposition of the neutral pivot point thus results. In contrast to thepreceding example illustrated in FIGS. 6A to 6C, the neutral pivot pointlies on scale T. A rotation or tilting of scanning unit AEH about apoint situated there does not cause a position offset.

The two examples described with reference to FIGS. 6A to 6C and 7A to 7Cillustrate that the neutral pivot point in an optical position-measuringdevice constitutes an important geometrical variable for any scanningvariant. More specifically, these two examples illustrate that theneutral pivot points in different scanning operations need notnecessarily have to coincide.

Therefore, the following may be stated: if the system in an opticalposition-measuring device is tilted about the neutral pivot point, thenthe measured position remains unchanged; and if the system is tiltedabout some other point, then the measured position changes without anactual position change being present.

Tilting in this case may include either tilting of the scanning unit orthe detection unit or tilting of the grating measuring standard.

According to example embodiments of the present invention, the proceduredescribed in German Patent Document No. 11 2005 002 253, and U.S. Pat.No. 7,187,305, for the correction of eccentricity-related errors inrotatory position-measuring device based on the measurement of therotational-angle-dependent radial offset of the grating measuring, whichis carried out during a calibration operation, and the correction of theposition value, offset by 90°, by the radial-offset value, which takesplace during the measuring operation, is to be expanded to thecorrection of the tumbling error in an incident light scanningoperation. To this end, the radial scanning of the grating measuringstandard, which takes place in a calibration operation, has to acquireboth the eccentricity deviations and the tumbling deviations of therotating graduated disk in a correct manner.

In this context, for the correct detection of the tumbling motion, theshift in position of the azimuthal scanning (measuring direction alongthe x-axis) by an R_(y) tilt has to be of the same magnitude as theshift in position of the radial scanning (measuring direction along they-axis) by an R_(x) tilt. This condition follows from the provided 90°offset of the correction and ultimately means that the neutral pivotpoints of the azimuthal scanning and the radial scanning have to belocated at the same distance from the graduated disk or the gratingmeasuring standard. In other words, the neutral pivot points of thescanning of the grating measuring standard for determining therotational angle and the displacement have to lie in the same plane,with this plane being situated in parallel with the grating measuringstandard.

These correlations are able to be described by the followingrelationships.

To begin with, in an expansion of relationship 2, the following appliesto the measured rotational angle value of the azimuthal incident lightscanning:

φ_(meas)(θ)=θ+Δφ_(ecc)(θ)+Δφ_(tilt)(θ)  (Eq. 9)

in which θ represents the rotational angle of the graduated disk,φ_(meas)(Θ) represents the rotational angle value of the azimuthalscanning, Δφ_(ecc)(Θ) represents the eccentricity-related rotationalangle error, and Δφ_(tilt)(Θ) represents the tumbling-related rotationalangle error.

Added to the eccentricity-related rotational angle error Δφ_(ecc)(Θ) inthe case of the incident-light scanning of a reflective gratingmeasuring standard thus is the error contribution caused by thetumbling-related rotational angle error Δφ_(tilt)(Θ), which may bedescribed as follows:

$\begin{matrix}{{{\Delta\phi}_{tilt}(\theta)} = {{\frac{1}{R} \cdot \Delta}\; {z_{A} \cdot {R_{y}(\theta)}}}} & ( {{Eq}.\mspace{11mu} 10} )\end{matrix}$

in which Θ represents the rotational angle of the graduated disk,Δφ_(tilt)(Θ) represent the tumbling-related rotational angle error, Rrepresents the scanning radius, Δz_(a) represents the distance of theneutral pivot point of the azimuth scanning from the graduated disk, andR_(y)(Θ) represents the tilting of the graduated disk about the y-axisat the scanning point.

It then follows from relationships 9 and 10 that:

$\begin{matrix}{{\phi_{meas}(\theta)} = {\theta + {{\Delta\phi}_{ecc}(\theta)} + {{\frac{1}{R} \cdot \Delta}\; {z_{A} \cdot {R_{y}(\theta)}}}}} & ( {{Eq}.\mspace{11mu} 11} )\end{matrix}$

in which θ represents the rotational angle of the graduated disk,φ_(meas)(Θ) represents the rotational angle value of the azimuthalscanning, Δφ_(ecc)(Θ) represents the eccentricity-related rotationalangle error, R represents the scanning radius, Δz_(a) represents thedistance of the neutral pivot point of the azimuth scanning from thegraduated disk, and R_(y)(Θ) represents the tilting of the graduateddisk about the y-axis at the scanning point.

In this case the coordinate system is selected such that the centerpoint of the graduated disk lies in the coordinate origin and theazimuthal scanning point lies at the location having the coordinatesx=0, y=R.

Analogous to relationship 9, the following applies to measured valueΔr_(meas)(Θ) of the radial incident light scanning:

Δr _(meas)(Θ)=Δr _(ecc)(θ)+Δr _(tilt)(θ)  (Eq. 12)

in which θ represents the rotational angle of the graduated disk,Δr_(meas)(Θ) represents the measured value of the radial incident lightscanning, and Δr_(ecc)(Θ) represents the eccentricity-related radialmeasured value.

In this context, the following applies to variable Δr_(tilt)(Θ), i.e.,the tumbling-related radial measured value:

Δr _(tilt)(θ)=Δz _(R) ·R _(x)(θ)  (Eq. 13)

in which θ represents the rotational angle of the graduated disk,Δr_(tilt)(Θ) represents the tumbling-related radial measured value,ΔZ_(R) represents the distance of the neutral pivot point of the radialscanning from the graduated disk, and R_(x)(Θ) represents the tilting ofthe graduated disk about the x-axis at the scanning point.

It should be noted that the measured value of the radial incident-lightscanning Δr_(meas)(Θ) according to relationship 12 includes both theactual eccentricity-related radial deflection of graduated diskΔr_(ecc)(Θ) and the tumbling-related radial shift of the light pattern,which is denoted by Δr_(tilt)(θ) and is referred to as tumbling-relatedradial measured value in the following text.

It then follows from relationships 12 and 13:

Δr _(meas)(θ)=Δr _(ecc)(θ)+ΔZ _(R) ·R _(x)(θ)  (Eq. 14)

in which θ represents the rotational angle of the graduated disk,Δr_(meas)(Θ) represents the measured value of the radial incident lightscanning, Δr_(ecc)(Θ) represents the eccentricity-related radialmeasured value, ΔZ_(R) represents the distance of the neutral pivotpoint of the radial scanning from the graduated disk, and R_(x)(Θ)represents the tilting of the graduated disk about the x-axis at thescanning point.

The tumbling motion of the graduated disk is described by the followingrelationship:

$\begin{matrix}{{R_{x}(\theta)} = {R_{y}( {\theta + \frac{\pi}{2}} )}} & ( {{Eq}.\mspace{11mu} 15} )\end{matrix}$

in which θ represents the rotational angle of the graduated disk,R_(x)(Θ) represents the tilting of the graduated disk about the x-axisat the scanning point, and R_(y) (Θ) represents the tilting of thegraduated disk about the y-axis at the scanning point.

If one divides relationship 14 by R and inserts relationship 5 andrelationship 15 into relationship 14, then the following results:

$\begin{matrix}{{{\frac{1}{R} \cdot \Delta}\; {r_{meas}(\theta)}} = {{{\Delta\phi}_{ecc}( {\theta + \frac{\pi}{2}} )} + {{\frac{1}{R} \cdot \Delta}\; {z_{R} \cdot {R_{y}( {\theta + \frac{\pi}{2}} )}}}}} & ( {{Eq}.\mspace{11mu} 16} )\end{matrix}$

An eccentricity and tumbling correction according to the afore-describedmethod presupposes that the tumbling contributions in the azimuthscanning (relationship 11) and in the radial scanning (relationship 16)are identical, that is to say:

Δz _(R) =Δz _(A)  (Eq. 17)

in which Δz_(a) represents the distance of the neutral pivot point ofthe azimuth scanning from the graduated disk and Δz_(R) represents thedistance of the neutral pivot point of the radial scanning from thegraduated disk.

A complete angle correction of eccentricity and tumbling deviations isable to be carried out analogous to relationship 6 according to thefollowing relationship:

$\begin{matrix}{{\phi_{corr}(\theta)} = {{\frac{1}{R} \cdot \Delta}\; {r_{meas}(\theta)}}} & ( {{Eq}.\mspace{11mu} 18} )\end{matrix}$

in which θ represents the rotational angle of the graduated disk,ϕ_(corr)(Θ) represents the rotational-angle-dependent correction value,R represents the scanning radius, and Δr_(meas)(Θ) represents themeasured value of the radial incident light scanning.

The angle θ may again be approximately replaced by the measured (faulty)angle value φ_(meas)(Θ). Thus, the following results for the output,corrected angular position φ_(out):

$\begin{matrix}{\phi_{out} = {\phi_{meas} - {\phi_{corr}( {\phi_{meas} - \frac{\pi}{2}} )}}} & ( {{Eq}.\mspace{11mu} 19} )\end{matrix}$

in which (pout represents the output, corrected angular position,φ_(meas)(Θ) represents the rotational angle value of the azimuthalscanning, and φ_(corr)(Θ) represents the rotational-angle-dependentcorrection value.

If the above relationship 17 with regard to equal distances of theneutral pivot points of both scans from the graduated disk or thegrating measuring standard is not observed, then the describedcorrection does compensate for the eccentricity-related rotational angleerror Δφ_(ecc)(Θ) but not for the tumbling-related rotational angleerror Δφ_(tilt)(Θ) (See, e.g., FIG. 5). The remaining residual error islarge especially if a cost-effective production of the shaft and/or thegraduated disk driving collar including correspondingly large tolerancesis desired and large tumbling motions occur as a result.

In summary, the optical position-measuring device for acquiring therotational angle between two objects that are able to rotationally moverelative to each other may be characterized as follows. For example, thecorresponding position-measuring device has a rotating graduated diskincluding a grating measuring standard, which is arranged as areflection grating. From its scanning, it is possible to obtain positioninformation both about an azimuthal rotary movement about the axis ofrotation and a radial displacement of the grating measuring standard. Atleast one detection unit is used for scanning the rotating gratingmeasuring standard in order to determine the azimuthal rotational angleas well as a radial displacement of the grating measuring standard.During a calibration operation, using a signal processing unit, which isappropriately configured in terms of its software and/or hardware, theradial displacement of the graduated disk is ascertained across arotation as a function of the rotational angle after the graduated diskas well as the detection units have been mounted in the respectiveapplication. The measured values regarding the radial displacement ofthe graduated disk obtained in the process are then stored in the formof a table in a memory of the signal processing unit; it is furthermorepossible to store a corresponding correction curve also in the form ofinterpolation points, for instance. During a measuring operation andusing the signal processing unit, the measured rotational angle value ofthe azimuthal scanning is corrected by the correction value, offset by90°, from the memory for eccentricity- and tumbling-related errors,e.g., according to relationship 19, and a corrected angular positionφ_(out) is output. The correction may also be performed by a linearinterpolation between the interpolation points stored in the memory.Instead of a correction via interpolation points, a correction mayalternatively also be obtained using a sinusoidal or cosine-shapedcorrection function, in which case its amplitude and phase position isdetermined from measured values Δr_(meas) and a corresponding fit. Thisprocedure, and in particular the desired tumbling compensation in thecase of incident light scanning, requires the neutral pivot points ofthe scanning of the grating measuring standard for a determination ofthe rotational angle and displacement to be situated in the same planeand in parallel with the grating measuring standard. If this is notensured, the output angular position (pout would then be corrected to aninsufficient or an excessive degree.

In FIGS. 8A and 8B, the procedure in a calibration operation (FIG. 8A)and in a measuring operation (FIG. 8B) is illustrated schematically foran optical position-measuring device.

According to FIG. 8A, in a calibration operation, while the graduateddisk or the grating measuring standard is rotating across a fullrotation, the signals for the radial displacement and for the rotationalangle of the graduated disk are generated in method steps S10 a, S10 bvia the corresponding scans. The corresponding signals are denoted byS_(r) (radial displacement) and S_(φ) (azimuthal rotational angle). Inmethod steps S11 a, S11 b, generated signals S_(r), S_(φ) areinterpolated in an appropriately configured signal processing unit andconverted into corresponding position signals Δr_(meas), φ_(meas), inwhich case Δr_(meas) denotes the position value of the radialmeasurement and φ_(meas) denotes the position value of the azimuthalmeasurement. In subsequent method step S12, a correction table is filledin in a memory of the signal processing unit, for which purpose acorrection value φ_(corr)(θ) is calculated for each angle θ which isused for the correction of the eccentricity- and tumbling-relatedrotational angle errors. Correction values φcorr(θ) may also be recordedonly at certain interpolation points across the circumference of thegraduated disk.

In method step S12, with the aid of a fit, it is also possible to obtainparameters of a (e.g., sinusoidal) correction function such as anamplitude and a phase from the position signals Δr_(meas), φ_(meas)recorded at certain interpolation points.

In FIG. 8B, the measuring operation of a position-measuring device isschematically illustrated. No acquisition of the radial displacement ofthe graduated disk takes place any longer in the measuring operation.According to method step S20, only the generation of signals S_(φ) withregard to the azimuthal rotational angle of the graduated disk isprovided. Signals S_(φ) are interpolated in method step S21 via thesignal processing unit and converted into position signals φ_(meas). Inmethod step S22, using correction values φ_(corr)(θ) according to theindicated relationship from method step S12 of the calibration operationor a correction function, correction value φ_(corr) for the respectiverotational angle Θ is ascertained via the signal processing unit andoffset in method step S23 together with measured value φ_(meas) so as toproduce output, corrected angular position φ_(out) according to theindicated relationship. Since the correction table is populated only ata finite number of interpolation points, the ascertainment of thecorrection value in method step S22 generally requires an interpolation,e.g., of conventional type.

FIGS. 9A, 9B, 10A, and 10B schematically illustrate example embodimentsof optical position-measuring devices. The two exemplary embodimentsfirstly differ in the used grating measuring standard and secondly inthe scanning for the acquisition of the azimuthal rotational angle andthe radial displacement of the grating measuring standard or graduateddisk.

The exemplary embodiment illustrated in FIGS. 9A and 9B uses a graduateddisk 10 having a grating measuring standard, such as that described, forexample, in German Patent Document No. 11 2005 002 253, and U.S. Pat.No. 7,187,305.

According to the top view of the graduated disk of FIG. 9A, gratingmeasuring standard 11, which is arranged as a reflection grating, has aradial graduation 11.1 situated on the inside and an adjacently situatedannular graduation 11.2 disposed on the outside. The two graduations11.1, 11.2 are disposed in two separate ring-shaped tracks on graduateddisk 10 in this instance. The radial graduation 11.1 includes radiallyoriented grating regions having different reflective properties for thelight incident upon them, and the annular graduation 11.2 includesring-shaped grating regions. The grating regions shown as light regionsin the different graduations 11.1, 11.2 have a highly reflectiveconfiguration, while the dark grating regions have a low reflectivity.Reference numeral 13 in FIG. 9A denotes the scanning point of a firstdetection unit on radial graduation 11.1. The first detection unit isused for scanning radial graduation 11.1 and for measuring azimuthalangle θ of graduated disk 10 during a calibration and measuringoperation. Reference numeral 14 in FIG. 9A denotes the scanning point ofa second detection unit on annular graduation 11.2. The second detectionunit is used for scanning annular graduation 11.2 and thus for measuringthe radial deflection of graduated disk 10 during a calibrationoperation.

FIG. 9B is a side view of the position-measuring device. As illustrated,graduated disk 10 together with grating measuring standard 11 disposedthereon in the form of radial and annular graduation 11.1, 11.2 istilted about pivot point D, which results in a tumbling motion ofgraduated disk 10 during the rotation about the axis of rotation.Indicated by dashed lines in FIG. 9B is non-tilted graduated disk 10′ inthe case of an ideal placement. Also illustrated in FIG. 9B is firstdetection unit 22, which is allocated to a scanning unit 20 and used forscanning radial graduation 11.1. Reference numeral 23 denotes a seconddetection unit, which is used for scanning annular graduation 11.2. Thetwo detection units 22, 23 include optoelectronic detectors in eachcase, which are arranged as structured photodetectors, for instance. Inthis exemplary embodiment, the two detection units 22, 23 share a lightsource 21, which is centrically situated in scanning unit 20 on acircuit board 26 and emits beam bundles in divergent form in thedirection of graduated disk 10, where the beam bundles are reflectedonto the two detection units 22, 23 by the two tracks of gratingmeasuring standard 11.

In addition, a signal processing unit 30, which is allocated to theposition-measuring device, is schematically illustrated in FIG. 9B. Thesignal processing unit 30 assumes the further processing of signalsS_(r), S_(φ) regarding the radial displacement of the graduated disk andregarding the azimuthal rotational angle acquired by detection units 22,23. Via the two interpolation units 31, 32, measured value Δr_(meas) ofthe radial deflection as well as measured value φ_(meas) regarding therotational angle of graduated disk 10 are able to be determined insignal processing unit 30 during a calibration and measuring operationand be further processed according to the afore-described procedure withthe aid of unit 33 so as to form an output angular position φ_(out),which is corrected for eccentricity and tumbling.

The neutral pivot point of the scanning for acquiring the azimuthalrotational angle via first detection unit 22 in this exemplaryembodiment lies in the same plane as the neutral pivot point of thescanning for acquiring the radial deflection of graduated disk 10 viasecond detection unit 23. Specifically, both neutral pivot points lie indetection plane 25 of the two detection units 22, 23, and thus inparallel with grating measuring standard 11.

It should also be mentioned in connection with this exemplary embodimentthat the radial scanning using the illumination direction tilted in theradial measuring direction does not cause any additional measuring errorby the distance changes that go hand-in-hand with the tumbling ofgraduated disk 10. This is ensured by divergent light source 21 situatedin detection plane 25.

FIGS. 10A and 10B illustrates an example embodiment of aposition-measuring device, which, similar to the previous example, onceagain show the plan view of graduated disk 110 as well as a side view ofa position-measuring device in connection with further components of theposition-measuring device. Only the main differences from the firstexemplary embodiment will be addressed in the following text. In allother respects, however, reference is made to the description of thefirst exemplary embodiment as well as FIGS. 9A and 9B.

As far as grating measuring standard 111 and the associated scanning ordetection unit are concerned, which are used in this exemplaryembodiment, reference to German Patent Document No. 10 2018 200 449 andU.S. Patent Application Publication No. 2019/0219422, each of which isexpressly incorporated herein in its entirety by reference thereto.

As illustrated in FIG. 10A, a grating measuring standard 111 isprovided, which has a configuration that differs from the previouslydescribed example embodiment and is situated in a ring-shaped track ongraduated disk 110. Reference numeral 14 in FIG. 10A denotes the singleprovided scanning point. Grating measuring standard 111, which in thisinstance is once again arranged as a reflection grating, includes stripeelements 111.1, 111.2, 111.3, . . . , which are disposed in an annularand periodic manner at a first measuring standard periodicity MV_(P1),with the stripe elements having a radial orientation in the longitudinalextension direction. Furthermore, for an absolute position encoding,stripe elements 111.1, 111.2, 111.3, . . . have a periodic structurealong their longitudinal extension direction, the periodic structurehaving structure elements 112, which have a second measuring standardperiodicity MV_(P2). For instance, the phase position of structureelements 112 may be used for an absolute position encoding of stripeelements 111.1, 111.2, 111.3, . . . , so that each stripe element 111.1,111.2, 111.3, . . . may be allocated a certain code value in thismanner. This makes it possible to provide code sequences across thecircumferential direction, which uniquely characterize an angularposition within 360°.

In contrast to the preceding exemplary embodiment, the grating regionsof grating measuring standard 111 shown as dark in FIG. 10A are highlyreflective and the light grating regions have a low reflectiveconfiguration.

Analogous to the previous exemplary embodiment, this exemplaryembodiment is illustrated in FIG. 10B in a schematic side view. Asillustrated in FIG. 10B, only one detection unit is provided on thescanning side in scanning unit 120 for scanning grating measuringstandard 111 disposed in a track. The detection unit includes only asingle divergent light source 121, e.g., an LED, as well as a singledetector system 122, which is periodically arranged along at least onedirection. Light source 121 is situated next to detector system 122 on acircuit board 126 in scanning unit 120.

In this case, central projection scanning using image scale β=2 isprovided for the optical scanning of grating measuring standard 111.Grating measuring standard 111 reflects the light emitted by lightsource 121 back into the detection plane of detector system 122. Imagescale β=2 exists when the distance from light source 121 to gratingmeasuring standard 111 exactly equals the distance from the plane ofgrating measuring standard 111 to the detection plane. In this case, thestructures on grating measuring standard 111 are projected onto detectorsystem 122 at precisely twice their size. In this regard, reference isalso made to the description of FIGS. 6 and 7 of thepreviously-mentioned German Patent Document No. 10 2018 200 449 and U.S.Patent Application Publication No. 2019/0219422.

In a modified variant, it is also possible to use a different imagescale β≠2, i.e., when the emission plane of the light source is notsituated exactly in the detection plane.

As in the first exemplary embodiment, the divergent light source, whichis disposed in the detection plane, ensures that the distance changesresulting from the tumbling motion of the graduated disk do not causeany additional measuring errors.

For example, detector system 122 is arranged as a two-dimensionaldetector system having a plurality of detector elements, which havemultiple detector columns with a plurality of detector elements in eachcase. The detector columns are periodically disposed along thering-shaped placement direction at a first detection periodicity, whilethe detector elements in the detector columns are periodically disposedat a second detection periodicity. In this context as well, reference isagain made to German Patent Document No. 10 2018 200 449 and U.S. PatentApplication Publication No. 2019/0219422.

In this exemplary embodiment, the provided scanning makes it possible toacquire the azimuthal rotational angle of graduated disk 110 and alsothe radial deflection of graduated disk 110 from a single track ofgrating measuring standard 111 on the graduated disk. In this regard,reference is once again made to the description of FIGS. 8a and 8b ofGerman Patent Document No. 10 2018 200 449 and U.S. Patent ApplicationPublication No. 2019/0219422, which describes obtaining information withregard to a tangential or radial offset of the graduated disk andscanning unit with the aid of such scanning.

The neutral pivot points in connection with the rotational angleacquisition and the acquisition of the displacement of graduated disk110 thus coincide. More specifically, the neutral pivot point lies indetection plane 125 of detector system 122 in this case.

In all other respects, the procedure for correcting the eccentricity-and tumbling-related rotational angle errors from acquired signalsS_(r), S_(φ) with regard to the radial displacement of the graduateddisk and with regard to the azimuthal rotational angle is performed asin the previously described example.

In addition to the above-described exemplary embodiments, there areadditional alternatives and options within the framework hereof.

For example, there is the option of recording the correction values notonly during the calibration operation but also of updating them on acontinuous basis during the measuring operation. The radial measuredvalues must be determined for this purpose and the correction valueshave to be appropriately adapted during the measuring operation as well.This adaptation may take place either directly to the full extent or ina damped manner by averaging using correction values from the past.

It is furthermore possible that the radial scanning and the azimuthalscanning do not take place at the same azimuthal position. In such acase, the correction described by relationship 19 will not take place ata 90° offset but at a corresponding different value, etc.

What is claimed is:
 1. An optical position-measuring device foracquiring an rotational angle between two objects that are rotationallymoveable relative to each other, comprising: a grating measuringstandard rotatable about an axis of rotation and including a reflectiongrating, position information relating to an azimuthal rotary movementabout the axis of rotation and relating to a radial displacement of thegrating measuring standard generatable in accordance with scanning ofthe grating measuring standard; and at least one detection unit adaptedto scan the grating measuring standard to determine an azimuthalrotational angle and the radial displacement of the grating measuringstandard; wherein neutral pivot points of scanning of the gratingmeasuring standard for determining the azimuthal rotational angle andthe radial displacement being located in a common plane that is arrangedparallel to the grating measuring standard, the neutral pivot pointdenoting a location about which the grating measuring standard or thedetection unit is tiltable without a position offset.
 2. The opticalposition-measuring device according to claim 1, wherein the gratingmeasuring standard includes a radial graduation and an annulargraduation arranged adjacent the radial graduation.
 3. The opticalposition-measuring device according to claim 2, wherein the at least onedetection unit includes a first detection unit adapted to scan theradial graduation and a second detection unit adapted to scan theannular graduation.
 4. The optical position-measuring device accordingto claim 1, wherein the grating measuring standard includes stripeelements arranged in an annular and periodic manner at a first measuringstandard periodicity, the stripe elements having a radial orientation ina longitudinal extension direction, and for absolute-position encoding,the stripe elements have a periodic structure with a second measuringstandard periodicity along the longitudinal extension direction.
 5. Theoptical position-measuring device according to claim 4, wherein thedetection unit includes a single light source and a single detectorsystem.
 6. The optical position-measuring device according to claim 5,wherein the detector system is arranged as a two-dimensional detectorsystem having a plurality of detector elements and a plurality ofdetector columns having multiple detector elements, the detector columnsbeing periodically arranged at a first detection periodicity along aring-shaped placement direction, and the detector elements in thedetector columns being periodically arranged at a second detectionperiodicity.
 7. The optical position-measuring device according to claim1, wherein the optical position-measuring device is configured foroptical scanning of the grating measuring standard as central projectionscanning using an image scale β=2, and includes a divergent light sourceand a detector system having a periodic configuration along at least onedirection.
 8. The optical position-measuring device according to claim1, further comprising a signal processing unit configured to: furtherprocess rotational-angle-dependent measured values, obtained during acalibration operation across at least one full rotation of the gratingmeasuring standard, into a radial displacement of the grating measuringstandard and store rotational-angle-dependent correction values in amemory of the signal processing unit, and utilize therotational-angle-dependent correction values stored in the memory in ameasuring operation for correction of the measured azimuthal rotationalangle with regard to existing eccentricity and tumbling errors.
 9. Theoptical position-measuring device according to claim 8, wherein thesignal processing unit is configured to utilize therotational-angle-dependent measured values with regard to a radialdisplacement of the grating measuring standard, obtained in acalibration operation, in a measuring operation for correction of arotational angle, offset by 90°, with regard to existing eccentricityand tumbling errors.
 10. The optical position-measuring device accordingto claim 8, wherein the signal processing unit is adapted to correct therotational angle for present eccentricity and tumbling errors accordingto:φ_(out)=φ_(meas)−φ_(corr)(φ_(meas)−π/2) in which φ_(out) represents anoutput, corrected angular position, φ_(meas)(Θ) represents therotational angle value of the azimuthal scanning, and φ_(corr)(Θ)represents the rotational-angle-dependent correction value.